How to animate multiple lines
You can use Curves and animate the Start bevel and End Bevel factors:


  These options determine where to start the Bevel operation on the
  Curve being beveled. Increasing the Start Bevel Factor to 0.5 will
  start beveling the Curve 50% of the distance from the start of the
  Curve (in effect shortening the Curve). Decreasing the End Bevel
  Factor by 0.25 will start beveling the Curve 25% of the distance from
  the end of the Curve (again, shortening the Curve).


These settings are in Properties > Object Data > Geometry: